New Moore-Like Bounds and Some Optimal Families of Abelian Cayley Mixed Graphs

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Issue date
2020-06-06
Author
Dalfó, Cristina
Fiol, Miguel Angel
López Lorenzo, Ignacio
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Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio; . (2020) . New Moore-Like Bounds and Some Optimal Families of Abelian Cayley Mixed Graphs. Annals Of Combinatorics, 2020, vol. 24, num. 2, p. 405-424. https://doi.org/10.1007/s00026-020-00496-2.
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Abstract
Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are Cayley graphs of abelian groups. Such groups can be constructed using a generalization to Zn of the concept of congruence in Z. Here we use this approach to present some families of mixed graphs, which, for every fixed value of the degree, have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal.
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http://hdl.handle.net/10459.1/69200
DOI
https://doi.org/10.1007/s00026-020-00496-2
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Annals Of Combinatorics, 2020, vol. 24, num. 2, p. 405-424
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